Tandem queue with three multiserver units and bulk service in unit III

In this paper a queueing model consisting of three units in series, with a finite number of parallel servers at each unit, is considered. Buffers of nonidentical finite capacity are available between the units. A buffer of infinite capacity is assumed to exist in front of the first unit. The occurrence times for all events have negative exponential distributions. Customers in the units I and II are served singly. Customers in the buffer zone between units II and III are served according to the general bulk service rule. The service times in the ith unit (i = 1, 2, 3) are assumed to be independently identically distributed random variables with negative exponential distributions with parameters μ_i(i = 1, 2, 3). The steady state probability vector of the number of customers in the queue is obtained using a modified matrix-geometric method. The stability condition is also obtained.